The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems ...

We present a new analytical method that systematically improves the convergence of path integrals of a generic N-fold discretized theory. Using it we calculate the effective actions S(p) for p< or =9, which lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit as 1/N(p). We checked this derived speedup in convergence by performing Monte Carlo si...

By recursively solving the underlying Schrödinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this, we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders that have not been accessible before. They can be used to substantially speed up numerical Monte Carlo calc...

In the present paper, we consider a fifth order method considered in Jaiswal (2016) to solve equations in Banach space under weaker assumptions. Using the idea of restricted convergence domains we extend the applicability of the method considered by Jaiswal (2016). Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. MS...

In this paper, we are interested in the analysis of regularized online algorithms associated with reproducing kernel Hilbert spaces. General conditions on the loss function and step sizes are given to ensure convergence. Explicit learning rates are also given for particular step sizes.

A consensus appears to have emerged in the literature that per capita income levels and/or levels of productivity in the industrialized market economies have converged significantly over the last century, and especially since the end of the second world war (see, e.g., Abramovitz, Baumol, Baumol and Wolff, De Long, Dollar and Wolff, Dowrick and Nguyen). The results of Abramovitz and Baumol, in ...

Convergence analysis for Turbo-equalization Aline Roumy, Alex J. Grant, Inbar Fijalkow, Paul D. Alexander, Didier Pirez Dept. of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA, Equipe de Traitement des Images et du Signal, ENSEA-University of Cergy-Pontoise, 95014 Cergy, France, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, SA 50...

in this research a new approach is proposed for elasto-plastic analysis of structures with truss elements. this method covers both perfectly plastic and hardening properties. the proposed technique uses substituting virtual loads instead of modifying the stiffness matrix. to solve this kind of problems, complementary programming is utilized. numerical examples demonstrate that elastoplastic ana...

The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we provide a guide for choosing an optimizer with respect to the given data set and the loss function. For analysis, we assume that the loss function is convex and it...